Performance deep dive

In this approach, we'll find out how to most efficiently calculate the value for Grains in Python.

The approaches page lists three idiomatic approaches to this exercise:

1. Using bit shifting
2. Using exponentiation
3. Using pow

Benchmarks

To benchmark the approaches, we wrote a small benchmark application using the timeit library.

bit shifting square 64:   1.2760140001773835e-07
bit shifting total 64:    6.096410000463947e-08
exponentiation square 64: 4.122742000035942e-07
exponentiation total 64:  6.094090000260621e-08
pow square 64:            4.2468130000634117e-07
pow total 64:             3.1965399999171494e-07

• Bit shifting was the fastest for square.
• Bit shifting and exponentiation were about the same for total.
• Exponentiation and pow were about the same for square.
• pow was significantly the slowest for total.

Benchmarks were also done to substitute if number not in range(1, 65): for if number < 1 or number > 64:.

bit shifting square 64:   2.708769000018947e-07
exponentiation square 64: 5.56936200009659e-07
pow square 64:            5.738279999932274e-07

Using if number not in range(1, 65): was over 125 nanoseconds longer than using if number < 1 or number > 64: for all approaches.